For real numbers x, let
f(x) = x + 2 if x > 3
f(x) = 2x - 3a if x <= 3
What must the value of a be to make the piecewise function f(x) continuous (which means that its graph can be drawn without lifting your pencil from the paper)?
We must have that the two lines intersect at x=3. Thus, x+2 = 2x-3a, so 5 = 6-3a, and a = 1/3. Thus, 2x-1 and x+2 intersect at (3,5) which is the endpoint of y in x>3, so a = 1/3.